Is it normal for my breasts to change shape or look strange when raising my arms over my head? Is this because of muscles pulling?

Shape and ligaments. The breasts are actually shaped like a comma with a tail out toward the armpit. Therefore, the shape will be different than when you have your arms down. This actually occurs because of ligaments attaching to the breasts called cooper's ligaments. You are at the age where you should have a breast exam and a baseline mammogram and I would recommend seeing your doctor for that.